Relative stability of zinc-blende and rocksalt structures: Crystalline and atomic pseudopotentials and the critical ionicity

Considering that the band structure of zinc-blende solids becomes of the rocksalt type when the antisymmetric and symmetric parts of the (111) and (311) pseudopotential Fourier components have the same absolute values, we discuss the relative stability of the two structures by comparing the wave vector of $V\left(111\right)\mathrm{}$ with the cation form-factor node $q_0^c$. An expression for the ionicity is also derived, resulting in $f_i=1.06\mathrm{}\frac{V_3^A}{V_3}$. This gives a value for the critical ionicity of 0.75, in good agreement with Phillips's value (0.785).